The NPR piece below mentions computational imagery for reconstructing the image but the papers on Grover Swartzlander publication page (including the one below) do not seem to indicate much in the way of L1 or similar regularization. It's just a question of time. Depending on how much they know about the glittering particles, it might be a compressive sensing or a compressive phase retrieval problem. Time will tell but I love the connection with some of technologies featured in "These Technologies Do Not Exist" page.